Universal battery parameterization to yield a non-linear equivalent circuit valid for battery simulation at arbitrary load
Introduction
The increasing demand for portable electronic devices in last years resulted in considerable increase of number of battery types, models and manufacturers. One can choose a battery for a particular application from a wide spectrum of candidate batteries such as lead acid, Ni–Cd, Ni-metalhydride (Ni-MH), Li-ion, and Li-polymer, etc. Batteries with similar chemistry produced by different manufacturers can also vary considerably in their properties, as shown by the authors of Ref. [1]for Li-ion batteries. So far the choice of a battery for particular application has been mostlydetermined based on discharge voltage, storage capacity (given for discharge method specified by manufacturer) as well as of the price of battery. These characteristics can give a rough impression of battery performance to the customer, but in many cases it would be misleading in regard to particular application, so large amount of additional information such as discharge curves at different currents, internal impedance and special features of discharge voltage profile are necessary. However, even in this case the evaluation of the battery for particular application remains only qualitative and subjective. A necessity to test an electrical device with real batteries made by each particular manufacturer still remains because all the standard features of battery has been obtained under steady state conditions. In certain cases this kind of test is impractical and costly so that a battery can be readily chosen after simply passing a test without performing further comparative tests. In particular, for instance, comparative tests for electric vehicle (EV) batteries are obviously not realistic due to heavy cost of manufacturing. The most time and cost efficient method to improve the confidence in the choice of the right battery substantially would be a digital simulation of the electrical device with a particular type of battery represented as an equivalent circuit. This approach will also improve the efficiency and stability of the device by matching impedance of its components with response of the chosen battery. This can be of large importance as shown in Ref. [2], and actually meaningful to simulate various situations arising from the failure of battery like the explosion of $1 billion Titan 4A rocket on August 4, 1998. All these can be done right in digital circuit simulator like SPICE, which has already become to an industrial standard and has been commonly used by electronics manufacturers for designing and testing their devices. A review on digital circuit simulators can be found in Ref. [3].
Unfortunately, the existing equivalent circuits for batteries are oversimplified and designed for the test of the electrical circuit itself rather than battery. Usually they comprise a constant voltage source in series with a resistor, which is valid only at DC conditions and in very short time because voltage change due to discharge of the battery is not considered. A more detailed approach which stores of battery discharge profiles at different discharge rates as a numerical table was proposed to use in a battery model for SPICE simulator in Ref. [4]. Although this method may correctly describe the constant current discharge of battery, it is not possible to treat charge/discharge processes of short time constants or transient conditions like pulse discharge.
A different approach to provide a representation for batteries including discharge voltage and internal resistance profile is disclosed in Ref. [5]for the purpose of using it in hardware simulator of thermal batteries. Similarly, Stoynov et al. [6]developed a step-by-step procedure obtaining parameters of a function which describes a simplified pulse current response at different states of charge, and used this parameters for stepwise prediction of the terminal voltage of battery. These models are valid in case of long time DC discharge but not in case of transient discharge conditions which occurs in many important application to portable devices like mobile phones, lap-top computers, power tools as well as in growing EV applications.
There has been a battery simulation method which partially considers the transient effects in order to predict open-circuit voltage of lead–acid batteries under dynamic discharge conditions [7]. This method includes measurements of charge and discharge voltage profiles at different currents and determination of five parameters for an equation which approximates the dependence of voltage upon total consumed/accumulated charge of lead–acid battery. The serial resistance is additionally determined to describe voltage behavior at charging or discharging conditions. Special equations have been used for different discharge modes, so the model can not be used directly under arbitrary load conditions. The applicability of the model is restricted to lead–acid batteries because it explicitly assumes a particular equation for voltage discharge profile. The simplification of diffusion hindrance to a serial resistance is also not sufficient in case of Li-ion batteries in which the transient time constants are comparable to total discharge time.
Obviously, there is a need for a model or an equivalent numerical representation of battery practically applicable and theoretically valid for digital simulation of all kind of batteries, in combination with arbitrary electrical load at wide range of electrical current densities and time-constants as well as for all depths of discharge. The model should be formalized in such a way that it can be directly used in electric circuit simulators. A standard automatic procedure to obtain all model parameters of a battery sample is also desired. In this work, we developed and tested a method corresponding to above requirements. Theoretical and experimental background of physically relevant impedance model used in this method is given in Refs. 8, 9.
Section snippets
Basic considerations
The process of energy storage in a battery, independent of particular chemistry, includes several common steps. The most important of these are (a) ionic charge conduction through electrolyte in pores of active layer and electronic charge conduction through conductive part of active layer, (b) electrochemical reaction on the interface of active material particles including electron transfer, and (c) diffusion of ions or neutral species into or out of electrochemical reaction zone. The
Experimental
The 18650 size Li-ion battery samples manufactured by Sony, Sanyo and Matsushita were obtained from commercially available cellular phone battery packs. All batteries had the capacity of 1350 mA h at the maximal charging voltage of 4.2 V and discharge rate of C/5. The AA-size Hitachi Ni-MH batteries had the rated capacity 1100 mA h at maximal voltage 1.2 V and discharge rate of C/5. Fresh batteries were 10 times cycled to reach relatively non-varying impedance and charge capacity before
Comparison of numerical and experimental results
In order to evaluate the performance of presented battery parameterization method, a parameterization of Sony, Matsushita and Sanyo 18650-size Li-ion batteries as well as Hitachi AA-size Ni-MH battery has been performed using described steps. Experimental impedance spectra for different discharge levels measured at Sony Li-ion battery are shown as an example in Fig. 3 and a numerical image of the battery as a set of parameters is shown in Table 1.
The obtained numerical images were used to
Discussion
The goal of this work is to create a model which provides a practical and sufficiently exact representation of a battery at any load conditions including transient conditions and an automatic measurement procedure which provides all necessary parameters without destroying the battery or exactly knowing its internal chemistry and configuration. However, these two requirements can possibly be conflicting. To provide an exact representation of battery under transient conditions it is necessary to
Conclusion
A new method for numerical representation of a battery by measurements of impedance spectra and equilibrium voltage profile and by non-linear fitting of impedance spectra into physically relevant equivalent circuit for the battery is developed. An assumption to represent both cathode and anode as one transmission line turned out be a sufficiently correct approximation both for small-signal analysis (linear case) and processes including considerable battery discharge (non-linear case). Tests
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2017, Electrochimica ActaCitation Excerpt :However, these data-driving EOL models have no definite physical-chemical meanings and are only valid for a specific battery system and working condition [35,36]. The equivalent circuit models in view of OCV have also been widely investigated, which is a universal modeling approach to predicting the EOL of LIBs based on a fixed equivalent circuit (EC) [37–39] for the electrochemical impedance spectra (EIS). For example, Pei et al. [40] developed an OCV estimation method based on a least square algorithm for a second order equivalent circuit model.